Completeness of coherent state subsystems for nilpotent Lie groups

Journal article (2022)

Authors

J.T. van Velthoven Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2022 J.T. van Velthoven
DOI: https://doi.org/10.5802/crmath.342
More Info
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

Let G be a nilpotent Lie group and let π be a coherent state representation of G. The interplay between the cyclicity of the restriction πjΓ to a lattice ≤ G and the completeness of subsystems of coherent states based on a homogeneous G-space is considered. In particular, it is shown that necessary density conditions for Perelomov's completeness problem can be obtained via density conditions for the cyclicity of πjΓ.